We study the thermodynamics of black holes in the framework of non-commutative geometry, where spacetime fuzziness is modelled by smeared Lorentzian distributions. Corrected black hole solutions with this quantum fuzziness are obtained, and their thermodynamic analysis is performed. We show that the conventional first law of black hole thermodynamics is violated since the entropy deviates from the Bekenstein-Hawking form. Introducing a correction to the mass restores consistency, yielding a modified first law compatible with Bekenstein-Hawking entropy. Next, we investigate the effects of spacetime non-commutativity on the thermodynamic universality of these black holes. We demonstrate that non-commutativity modifies the standard universality relations of black holes and can induce thermodynamic stability by altering the underlying microscopic interactions. Our results suggest that quantum features of spacetime can have significant macroscopic consequences for black hole thermodynamics.

We investigate the thermodynamics, topology, and geometry of black holes in Lorentz-violating gravity. Modifications in the theory by perturbative parameter lead to coupled changes in horizon structure and thermodynamic behaviour, allowing us to derive generalized universal relations and explore implications for the Weak Gravity Conjecture. The thermodynamic topology reveals distinct topological charges, with photon spheres identified as robust topological defects. Our analysis shows that the Ruppeiner curvature remains universally negative across thermodynamic ensembles, indicating dominant attractive interactions among microstructures. This ensemble-independent behaviour highlights a fundamental thermodynamic universality in Lorentz-violating settings. Together, these results provide a consistent and rich framework for understanding black hole microphysics and gravitational consistency in modified theories. We further study the motion of timelike test particles in these black hole spacetimes by analyzing the effective potential shaped by the Lorentz-violating couplings. The resulting dynamics reveal the existence of bound orbits and stable circular trajectories, with the location of the innermost stable circular orbit and turning points significantly influenced by the parameters $\ell_{1,2}$, and the cosmological constant. Numerical simulations of trajectories in the $x-y,\,x-z$, and 3D planes show precessing, bounded, and plunging orbits, depending on the particle's specific energy and angular momentum. These results highlight how Lorentz-violating effects alter the structure of geodesic motion and provide potential observational signatures in the dynamics of massive particles near black holes.

Ethylene glycol is a prebiotically relevant complex organic molecule detected in interstellar and cometary environments, yet quantitative low-energy electron-ethylene glycol scattering data remain limited for astrochemical modeling. This work presents an R-matrix study of low-energy electron collisions with ethylene glycol over the 0 to 12 eV energy range, using static exchange (SE), static exchange plus polarization (SEP), and configuration interaction (CI) models with 6-311G* and cc-pVTZ basis sets. We compute elastic, excitation, and differential cross sections within a close coupling framework. The dataset offers benchmark inputs for astrochemical models, supporting interpretation of ethylene glycol abundances in space and refining constraints on electron-induced prebiotic pathways.

Aminoacetonitrile occupies a prime importance in the interface between astrochemistry and prebiotic chemistry. Its detection in the ISM establishes it as part of the organic inventory of star-forming regions, while its role as a glycine precursor highlights its significance for origins-of-life scenarios. In this work, electron scattering from aminoacetonitrile has been studied using the R-matrix method in the low-energy range from 0 to 10 eV. The calculations were carried out within the C_s point group using static-exchange (SE), static-exchange plus polarization (SEP), and configuration interaction (CI) models, with two basis sets (6-311G* and cc-pVTZ). Various scattering observables such as elastic, excitation, momentum transfer, and differential cross sections were examined. Since aminoacetonitrile is a prebiotically relevant molecule, these findings provide valuable insight into electron-driven processes in complex organic systems and form a theoretical foundation for future work on electron-induced reactivity in prebiotic and astrophysical environments.

We investigate the heat kernel method for one-loop effective action following the Seeley-DeWitt expansion technique of heat kernel with Seeley-DeWitt coefficients. We also review a general approach of computing the Seeley-DeWitt coefficients in terms of background or geometric invariants. We, then consider the Einstein-Maxwell theory embedded in minimal $\mathcal{N}=2$ supergravity in four dimensions and compute the first three Seeley-DeWitt coefficients of the kinetic operator of the bosonic and the fermionic fields in an arbitrary background field configuration. We find the applications of these results in the computation of logarithmic corrections to Bekenstein-Hawking entropy of the extremal Kerr-Newman, Kerr and Reissner-Nordstrom black holes in minimal $\mathcal{N}=2$ Einstein-Maxwell supergravity theory following the quantum entropy function formalism.

In this paper, we have computed the logarithmic corrections of entropy for the near-extremal Kerr-Newman black holes in $\mathcal{N}=2$ supergravity theory applying the Euclidean path integral approach in the near-horizon geometry. In the near-horizon extremal Kerr geometry, analogous to the $AdS_{2} \times S^2 $ structure, there exists a set of normalizable zero modes associated with reparametrizations of boundary time. The one-loop approximation to the Euclidean near-horizon extremal Kerr partition function exhibits an infrared divergence due to the path integral over these zero modes. Carrying out the leading finite temperature correction in the near-horizon extremal Kerr scaling limit, we control this divergence. Considering the near-extremal near-horizon geometry as a perturbation around the extremal near-horizon geometry, we determine these corrections implementing a modified heat kernel approach which involves both the extremal and near-extremal corrections and is novel in the literature for the charged rotating black holes in supergravity theory. This result should be reproduced by any microscopic theory that explains the entropy of the black hole.

Convection-driven flows in planetary interiors exhibit rich dynamics owing to multiple spatio-temporally varying forcing conditions and physical constraints. In particular, the churning of liquid metals in the Earth's outer core, responsible for the dynamic geomagnetic field, is subjected to lower mantle thermal heterogeneity. Besides, the plausible existence of a stable stratification layer below the mantle influences the columnar convection. These additional symmetry-breaking constraints, motivated from geophysical scenario of the Earth's thermal core--mantle interaction, modulate the otherwise periodic and axially invariant convection flow patterns. Thus, the present study focuses on qualitative characterization and parametric quantification of rotating penetrative convection in the presence of magnetic induction effects with an aim to understand the role of the lower mantle on core convection thermally. Using complementing computational and theoretical calculations, the present study estimates the depth of penetration in bounded and unbounded fluid domains. Apart from qualitative differences in convective flow patterns from the reference homogeneous configurations, the additional constraints spatially modulate the extent of penetration into stable regions. Confinement effects, adding to the damping of penetrative convection, arising out of boundary constraints are quantified for bounded geometry. Appropriate normalizations, implemented to eliminate such effects, result in amended penetration depth estimates that align with the qualitative characteristics obtained for unbounded domains. Exact closed-form expressions for the depth of penetration are obtained, providing insights into the role of individual contributions of multiple physical constraints. Implications are speculated for realistic, yet unreachable, regimes of geophysical conditions of planetary cores.

We investigates the effect of accretion of cosmic fluid on the evolution of Primordial Black Holes (PBHs) within the framework of Modified gravity theories. We consider a general form of the Hubble parameter, reflecting a general class of modified gravity theories and bouncing models. We then study the effect of such modified dynamics on PBH in the presence of Hawking radiation and accretion of surrounding materials. We investigate how the evolution of PBHs is influenced by accretion across different cosmological eras, considering the radiation, matter, and dark energy-dominated phases like phantom and quintessence for linear equation of state. We further incorporated Non-linear Equations of State such as Chaplygin Gas, Modified Chaplygin gas, Van der Waals model, Polytropic Fluid model. The study systematically analyzes the mass variation of PBHs in the presence of such different cosmological environments. The results will contribute to the understanding of PBH formation and evolution in modified theory of gravity, and their possibility of being detected with future experiments.

This work employs the quantum extremal surface framework to compute the Page curve for black holes corrected by non-extensive entropy. The entropy of Hawking radiation increases linearly with time, leading to the persistence of the information paradox for non-extensive entropy-corrected black holes. At late time, we extremize the generalized entropy functional; incorporating contributions from both matter and the quantum extremal island, we establish that the entanglement entropy of Hawking radiation saturates to the non-extensive extension of the Bekenstein-Hawking entropy. Finally, we study the dependence of non-extensive parameters on the Page time.

In this manuscript, an attempt has been made to understand the effects of prey-taxis on the existence of global-in-time solutions and dynamics in an eco-epidemiological model, particularly under the influence of slow dispersal characterized by the $p$-Laplacian operator and enhanced mortality of the infected prey, subject to specific assumptions on the taxis sensitivity functions. We prove the global existence of classical solutions when the infected prey undergoes random motion and exhibits standard mortality. Under the assumption that the infected prey disperses slowly and exhibits enhanced mortality, we prove the global existence of weak solutions. Following a detailed mathematical investigation of the proposed model, we shift our focus to analyse the stability of the positive equilibrium point under the scenario where all species exhibit linear diffusion, the infected prey experiences standard mortality, and the predator exhibits taxis exclusively toward the infected prey. Within this framework, we establish the occurrence of a steady-state bifurcation. Numerical simulations are then carried out to observe this dynamical behavior. Our results have large scale applications to biological invasions and biological control of pests, under the prevalence of disease in the pest population.

The aim of this letter is to study the universal thermodynamics and criticality of charged AdS black holes with string clouds in the bulk and in the boundary conformal field theory (CFT). For this system, we determined the critical quantities and noticed that the free energy in the bulk exhibits swallow tail behavior. In the boundary CFT, the presence of second order phase transition is observed. At constant charge, the heat capacity is finite in the bulk but diverges at critical points in the boundary CFT. Furthermore, we tried to determine the nature of interactions between black hole molecules in the boundary CFT and in the bulk, which is novel for charged AdS black holes with string clouds.

The present study explores the onset of the Rayleigh-Taylor instability (RTI) and Kelvin-Helmholtz Rayleigh-Taylor instability (KHRTI) with highly-resolved direct numerical simulations of two setups which consider air at different temperatures (or densities) and/or velocities in two halves of three-dimensional cuboidal domains. The compressible Navier-Stokes equations are solved using a novel parallel algorithm which does not involve overlapping points at sub-domain boundaries. The pressure disturbance field is compared during onset of RTI and KHRTI and corresponding convection- and advection-dominated mechanisms are highlighted by instantaneous features, spectra, and proper orthogonal decomposition. The relative contributions of pressure, kinetic energy and rotational energy to the overall energy budget is explored for both instabilities, revealing acoustic trigger to be the incipient mechanism for both RTI and KHRTI. The nonlinear, spatio-temporal nature of the instability is further explored by application of a transport equation for enstrophy of compressible flows. This provides insights into the similarities and differences between the onset mechanisms of RTI and KHRTI, serving as a benchmark data set for shear and buoyancy-driven instabilities across diverse applications in geophysics, nuclear energy and atmospheric fluid dynamics.

In this paper, we study the influence of string fluids on the extended thermodynamic structure and microscopic interactions of Hayward black holes by employing thermodynamic geometry as an empirical tool. Using the novel equation of state obtained for regular black holes surrounded by string fluids, we analyze the extended phase space with enthalpy as the central thermodynamic potential. By examining the behavior of the normalized Ruppeiner curvature scalar $R_N$ in the temperature-volume $(T,V)$ plane, we analyzed the influence of the string fluid parameters on the microstructure of the black hole. Our analysis reveals that the presence of string fluids significantly modifies the dominant microscopic interactions, transitioning from attractive to repulsive regimes depending on the charge and volume of the black hole. We see that the thermodynamic curvature effectively detects critical points and phase transitions, reflecting the nature of repulsive or attractive interactions among black hole microstructures. We further investigate thermodynamic topology to provide a novel classification scheme for stability and phase behavior, delineating local stable and unstable regions in parameter space. We investigate the thermodynamic topology of Hayward-AdS black holes surrounded by string fluids, showing that the number and type of topological charges depend on the parameters $\epsilon$ and $b$, revealing phase transitions and stability characteristics encoded in the global topological charge $W$. This integrated study of the thermodynamic geometry and topology structure enhances the understanding of Hayward black holes surrounded by string fluids, showing overall thermodynamic stability and configuration with significant implications for holographic duality and potential astrophysical observations.

In this work, we examine the onset of thermodynamic chaos in Hayward AdS black holes with string fluids, emphasizing the effects of temporal and spatially periodic perturbations. We apply Melnikov's approach to examine the perturbed Hamiltonian dynamics and detect the onset of chaotic behavior within the spinodal regime of the $(P-v)$ plot. In the case of temporal perturbations induced by thermal quenches, chaos occurs for perturbation amplitude $\gamma$ exceeding a critical threshold that can be determined by charge $q$ and the string fluid parameter. From the equation of state of the black hole, a general condition can be established indicating that under temporal perturbations, the existence of charge is an essential prerequisite for chaos. In this regime, neutral Hayward black holes do not exhibit chaotic dynamics. However, regardless of the presence of charge, spatial perturbations result in chaotic behavior. The nonlinear interplay between the regularized core geometry and string fluids drives the formation of homoclinic and heteroclinic orbits in phase space, validating the persistence of chaos. The results obtained in this work, highlights the role of nonlinear matter fields and curvature regularization mechanisms in governing thermodynamic instability and the onset of chaos in Hayward black holes in AdS.

Recent scanning tunneling microscopy (STM) observation of U-shaped and V-shaped spectra (and their mixture) in superconducting Nd$_{1-x}$Sr$_x$NiO$_2$ thin films has been interpreted as presence of two distinct gap symmetries in this nickelate superconductor [Gu et al., Nat. Comm. 11, 6027 (2020)]. Here, using a two-band model of nickelates capturing dominant contributions from Ni-$3d_{x^2-y^2}$ and rare-earth (R)-$5d_{3z^2 - r^2}$ orbitals, we show that the experimental observation can be simply explained within a pairing scenario characterized by a conventional $d_{x^2-y^2}$-wave gap structure with lowest harmonic on the Ni-band and a $d_{x^2-y^2}$-wave gap with higher-harmonics on the R-band. We perform realistic simulations of STM spectra employing first-principles Wannier functions to properly account for the tunneling processes and obtain V, U, and mixed spectral line-shapes depending on the position of the STM tip within the unit cell. The V- and U-shaped spectra are contributed from Ni and R-bands, respectively, and Wannier functions, in essence, provide position-dependent weighing factors, determining the spectral line-shape at a given intra-unit cell position. We propose a phase-sensitive experiment to distinguish between the proposed $d$-wave gap structure and time-reversal symmetry breaking $d+is$ gap which yields very similar intra-unit cell spectra.

We study the production of the Higgs in a association with a vector ($V=W,Z$) via the VBF process, VBF-VH. In the Standard Model (SM), this process exhibits tree-level destructive interference between between $W$ and $Z$ mediated processes and is thus very sensitive to deviations in Higgs couplings to vector bosons. We study this process at both the HL-LHC as well as future high energy lepton colliders. We show in particular that the scenario where Higgs couplings have the same magnitude but opposite relative sign as in the SM, a scenario that is very difficult to distinguish without interference, can be probed with this process at either collider.

The existence of plate tectonics on the Earth is directly dependent on the internal viscosity contrast, mass of the planet, availability of liquid water and an internal heat source. However, the initial conditions of rotational velocity and revolutionary periodicity of the Earth around the Sun too must have been significant for the inception of plate tectonics. The initial orbital conditions of the Earth were significantly influenced by the diametrical processes of core segregation and Moon formation and that had probably led to the eventuality of initiation and persistence of plate tectonics. The change in the orbital conditions could have rendered the Earth to evolve in a near-linear trend so that the rotational periodicity of the planet (TP) could approach the time taken for the planet to travel one degree in its orbit around the Sun (T1degree), that is TP ~ T1degree. Such an optimal condition for the rotational and revolutionary periodicities could be essential for the development of plate tectonics on the Earth. This hypothesis has direct implications on the possibility of plate tectonics and life in extrasolar planets and potentially habitable solar planetary bodies such as Europa and Mars.

One of the most pressing societal issues is the fight against false news. The false claims, as difficult as they are to expose, create a lot of damage. To tackle the problem, fact verification becomes crucial and thus has been a topic of interest among diverse research communities. Using only the textual form of data we propose our solution to the problem and achieve competitive results with other approaches. We present our solution based on two approaches - PLM (pre-trained language model) based method and Prompt based method. The PLM-based approach uses the traditional supervised learning, where the model is trained to take 'x' as input and output prediction 'y' as P(y|x). Whereas, Prompt-based learning reflects the idea to design input to fit the model such that the original objective may be re-framed as a problem of (masked) language modeling. We may further stimulate the rich knowledge provided by PLMs to better serve downstream tasks by employing extra prompts to fine-tune PLMs. Our experiments showed that the proposed method performs better than just fine-tuning PLMs. We achieved an F1 score of 0.6946 on the FACTIFY dataset and a 7th position on the competition leader-board.